removed duplicated points, texture completely warped
This is possible to repair by recognizing which island on UV map isn't needed for unwrap and deleting adjacent vertices. It's preferable of course to avoid such situations and check for double vertices / faces' normals / holes in mesh / internal faces / non-manifold geometry etc. before starting unwrapping / rigging and so on.

The workflow consists in toggling between Keep UV and Edit mode mesh in sync modes in order to find selected vertices in UV map on the model. 


Split the window and set the newly opened editor to UV/Image Editor. See How to close windows for more info about closing / opening different editors inside Blender. In Edit mode select whole model with A.
In UV / Image Editor window select top islands of UV map because they don't preserve the unwrap, but do mess up the UV map and model when doubles are removed. In order to do that select them with RMB; to add to selection press Shift+RMB. You should end up with top islands selected. Grab them and the bottom ones will be revealed (and hence the doubles are present):


Move those islands somewhere so that they don't intersect with bottom ones. Check Keep UV and Edit mode mesh in sync in the header of the UV / Image Editor. Use B to box select the top ones. 

You'll notice several vertices selected on the bottom ones, deselect them with Box Select tool (because these are shared vertices by both islands, thus if you delete them you'll loose the geometry of original mesh, not only double vertices). Hover mouse over 3D Viewport and delete selected vertices.



Now UV map shoudn't react on removing doubles because mostly they were already deleted, with preserving unwrapped islands.

Blend file